Hi coltman,
To open directory use opendir, not open which is use for files and associated with a FILEHANDLES.
The code below uses recursive call to go through all the folders in a directory given.

#!/usr/bin/perl
use warnings;
use strict;
use Cwd qw(abs_path);

die "no directory provided " unless defined $ARGV[0];
my $path = abs_path $ARGV[0];

search_all_folder($path);

sub search_all_folder {
    my ($folder) = @_;
    if ( -d $folder ) {
        chdir $folder;
        opendir my $dh, $folder or die "can't open the directory: $!";
        while ( defined( my $file = readdir($dh) ) ) {
            chomp $file;
            next if $file eq '.' or $file eq '..';
            search_all_folder("$folder/$file");  ## recursive call
            read_files($file) if ( -f $file );
        }
        closedir $dh or die "can't close directory: $!";
    }
}

sub read_files {
    my ($filename) = @_;

    open my $fh, '<', $filename or die "can't open file: $!";
    while (<$fh>) {
        print $_, $/;
    }
}
[download]

Hope this helps.
UPDATE:
Like others have said before now, it will be half the work and a lot easiler to use module like File::Find like so:

use warnings;
use strict;
use Cwd qw(abs_path);
use File::Find qw(find);

die "no directory provided " unless defined $ARGV[0];
my $path = abs_path $ARGV[0];

find( \&search_all_folder, $path );

sub search_all_folder {
    chomp $_;
    return if $_ eq '.' or $_ eq '..';
    read_files($_) if (-f);
}

sub read_files {
    my ($filename) = @_;

    open my $fh, '<', $filename or die "can't open file: $!";
    while (<$fh>) {
        print $_, $/;
    }
}
[download]

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